In a shallow bowl, combine the flour, garlic powder, 1/2 teaspoon salt, and black pepper; dredge each chicken cutlet to lightly coat both sides.
Heat the olive oil in a large skillet over medium-high heat until hot.
Add the coated chicken to the skillet in a single layer and cook 3–4 minutes per side, until golden and cooked through; transfer the chicken to a plate and set aside.
Reduce heat to medium-high and melt the butter in the same skillet.
Add the sliced mushrooms, pressed garlic, and the remaining 1/2 teaspoon salt; cook, stirring occasionally, until the mushrooms release their liquid and it evaporates, about 4–6 minutes.
Pour in the heavy cream and stir in the grated Parmesan; bring to a rapid boil while stirring, cook 2 minutes, then reduce heat to low.
Return the chicken to the skillet, spoon sauce over the pieces, and simmer 3–5 minutes until the sauce thickens and the chicken is heated through.